Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e112.1 | |- (. ph ->. ps ). |
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e112.2 | |- (. ph ->. ch ). |
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e112.3 | |- (. ph ,. th ->. ta ). |
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e112.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
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Assertion | e112 | |- (. ph ,. th ->. et ). |
Step | Hyp | Ref | Expression |
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1 | e112.1 | |- (. ph ->. ps ). |
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2 | e112.2 | |- (. ph ->. ch ). |
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3 | e112.3 | |- (. ph ,. th ->. ta ). |
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4 | e112.4 | |- ( ps -> ( ch -> ( ta -> et ) ) ) |
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5 | 1 | vd12 | |- (. ph ,. th ->. ps ). |
6 | 2 | vd12 | |- (. ph ,. th ->. ch ). |
7 | 5 6 3 4 | e222 | |- (. ph ,. th ->. et ). |